Sig Sauer P230 inner pin stuck (plugged with broken punch) - How can it be removed?

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I will make this as short as possible. Purchased a very well used Sig P230 in stainless version and decided to disassemble it for a thorough cleaning job as I usually do with used firearms. Parts came off with quite easily until I went to remove the pin from the slide. I used a 1/16" Starrett pin punch and tapped the inner slide pin (Part #49 inner pin H.D according to parts diagram) in order to remove it. After quite a few taps and dropping lubricant on the pin it would not move. Hit it harder a few more times and it did not budge. Tried pulling the punch back out and it was stuck in the inner pin. Unfortunately after moving and twisting the punch slowly it broke off and left a small piece stuck in the pin. Went and tried on the other side and the same thing exact thing happened. I tried hammering with another punch from both sides, but this thing is really stuck and now the pin is plugged on both ends. I did not want to drill it not having a proper drill press. I do not have a hydraulic press either.
I have been able to do this with no problem on all my other Sig Sauer pistols but this was the first one I had a problem with.
Now for the questions.
The breech block can be removed from the P230 canít it? With the inner pin being plugged on both sides with a piece of the punch plugged on both ends what would you recommend would be the best way to get this removed or just leave it? If it is left the way could this be dangerous when being under pressure while firing?

Roll pins require the use of a specially-shaped punch, exactly so that what you've experienced won't happen.
The nose of the special punch is shaped in such a way that it will not enter the center of the roll pin, so it will not get stuck.

It is possible to shatter the broken-off pieces of the stuck punch(es), and then to pick them out. It's not an easy, simple job, though.
Your best bet is to take your mess to a qualified gunsmith, and let him figure a solution out. Whatever you pay him, it'll be worth it.

A long time ago, I broke a hardened screw off in a hole, in a soft-steel lockplate.
The jeweler whose shop was across the street from my own place had gotten his start as a machinist on board a WW2 submarine. I consulted him, and he suggested that I place the lockplate into a glass beaker containing a solution of styptic pencil (aluminum hydroxide, I believe) in water, and then to gently boil the stuff.
In about an hour, the hardened piece of screw almost fell out, all on its own. The threaded hole was almost unchanged, and was still completely functional.
He explained: The styptic material attacks hardened steel more avidly than it attacks soft steel, so the screw lost diameter faster than the lockplate lost its dimensions. He told me all about the chemistry involved, but I no longer remember it.
This technique, however, should be seen as a last resort. The penalties for a little bit of miscalculation would be disastrous. But it would work on your broken-off punch tips.